Fitting Laguerre Tessellations to the Microstructure of Cellular Materials

Abstract

Cellular materials are employed in many fields, ranging from medical technologies to aerospace industry. In applications, understanding the influence of the microstructures on the physical properties of materials is of crucial importance. Stochastic models are a powerful tool to investigate this link. In particular, random Laguerre tessellations (weighted generalizations of the well-known Voronoi model) generated by systems of non-overlapping balls have proven to be a promising model for rigid foams. Model fitting is based on geometric characteristics estimated from micro-computed tomographic images of the microstructures. More precisely, the model is chosen to minimize a distance measure composed of several geometric characteristics of the typical cell. However, with this approach, inference on the model parameters is time consuming and needs expert knowledge. In this talk, we investigate strategies leading to an automatic model fitting. Finally, this model fitting approach is applied to polymethacrylimide (PMI) foam samples.